The present invention relates to a method and apparatus for determining the relative phase of two waveforms and, more particularly, to an electricity metering method and apparatus for determining the phase of distorted voltage and current waveforms.
Electric power is typically generated at a remote, central generating facility and transported to the consumer over a distribution system. To reduce power transportation losses, a step-up, subtransmission transformer is used to increase the voltage and reduce the current for transmission over a transmission line. The actual transmission line voltage usually depends on the distance between the subtransmission transformers and the consumers of the electricity but is commonly in the range of 2–35 kilo-volts (“kV”). Distribution substation transformers and distribution transformers of an electric utility's secondary power distribution system reduce the voltage from the transmission line level to a distribution voltage for delivery and use by industrial, commercial, and residential customers. In the United States, for example, electric power is typically delivered to the consumer as a alternating current (AC) voltage ranging from 120 volts (“V”) to 660 V, depending upon the use. As generated, the fundamental AC voltage and current approximate 60 Hertz (“Hz”) sine waves over time.
The consumption of power by individual consumers and the performance of the distribution system are monitored by power meters. Power meters are used to monitor a number of electrical parameters related to power distribution and use, including the active power, the time rate of transferring or transforming energy, and the apparent power, the product of the root mean square (RMS) voltage and current. In addition, the reactive power, the product of the RMS voltage and the quadrature component of the current, and the power factor or quality factor, the ratio of active power to apparent power, are commonly monitored.
Power meters may also be used to measure the phase angle between the current and voltage waveforms. The phase angle expresses the temporal relationship of a cycle distinguishing feature of a first waveform, commonly an amplitude peak or a zero crossing, to the position of a corresponding feature in another waveform. As generated, the voltage and current waveforms are in phase and simultaneously reach zero, maximum, and minimum amplitudes. If the load is purely resistive, the voltage and current remain in phase. However, if the load is capacitive, the phase distinguishing feature of the current waveform will precede that of the voltage waveform and the phase angle is designated as leading. On the other hand, an inductive load produces a lagging phase angle with the phase distinguishing feature of the voltage waveform preceding that of the current waveform. The reactive power consumed by capacitive and inductive loads causes power losses in the transmission system and reduces the overall efficiency of the power distribution system. Phase angle measurement permits billing the consumer for reactive power losses and analysis of the nature of the load so that power conditioning equipment can be added to the system to reduce the reactive power losses.
Inductive, capacitive, and resistive loads have impedances that are independent of voltage and at any single frequency the impedances of these loads are linear. While an inductive or capacitive load will cause the relative phase angle of the voltage and current to change, the sinusoidal voltage and current waveforms are not distorted when an AC voltage is applied to an inductive, capacitive, or resistive load. Sinusoidal waveforms have definite zero crossings and amplitude peaks and, typically, either a zero crossing or an amplitude peak is selected as the distinguishing feature to temporally mark the cycles of a waveform when determining the phase angle or phase.
Referring to FIG. 1C, on the other hand, power electronic loads; including variable speed drives, rectifiers, inverters, and arc furnaces; draw current 60 in short abrupt pulses 62 rather than in a smooth sinusoidal manner and are characterized as non-linear. When a non-linear load is connected to a sinusoidal voltage, the current flow is not proportional to the instantaneous voltage and is not sinusoidal. The non-linearity of power electronic loads produce harmonics of the fundamental voltage sine wave. In a power distribution system, the expected frequency of the voltage or current, e.g., 50 Hz, 60 Hz, or 400 Hz, is conventionally referred to as the “fundamental” frequency, regardless of the actual spectral amplitude peak. Integer multiples of this fundamental frequency are usually referred to as harmonic frequencies or harmonics. Referring to FIGS. 1A and 1B, when a sine wave of the fundamental frequency 20 is combined with a plurality of harmonics 22, 24, 26, 28 the instantaneous amplitude of the resulting waveform 30 is a sum incorporating the instantaneous amplitude of the fundamental waveform and the corresponding instantaneous amplitudes of the harmonic waveforms. Determining the phase of a waveform relative to an amplitude peak or a zero crossing of a harmonically distorted waveform 30 is problematic because the contributions of higher frequency harmonics commonly produces a plurality of contemporaneous amplitude peaks 32, particularly in the vicinities of the expected amplitude peaks or zero crossings of the fundamental waveform. As a result of the dithering of the amplitude, the distorted wave commonly includes a plurality of contemporaneous zero crossings 34 and amplitude peaks 32. Extensive filtering to remove harmonic frequencies from the reference waveform or other computationally intensive signal processing, such as interpolation, is required to consistently distinguish a zero crossing or amplitude peak for a succession of cycles of a harmonically distorted waveform.
What is desired, therefore, is a method and apparatus for accurate and consistent determination of the phase angle relative to a harmonically distorted waveform.